Related papers: Analytical Discovery of Manifold with Machine Lear…

Large Language Model (LLM)-based Automated Program Repair (APR) has shown strong potential on textual benchmarks, yet struggles in multimodal scenarios where bugs are reported with GUI screenshots. Existing methods typically convert images…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

We present the Universal Latent Homeomorphic Manifold (ULHM), a framework that unifies semantic representations (e.g., human descriptions, diagnostic labels) and observation-driven machine representations (e.g., pixel intensities, sensor…

Natural systems with emergent behaviors often organize along low-dimensional subsets of high-dimensional spaces. For example, despite the tens of thousands of genes in the human genome, the principled study of genomics is fruitful because…

The accurate prediction of protein-ligand binding affinity is important for drug discovery yet remains challenging for multi-domain proteins, where inter-domain dynamics and flexible linkers govern molecular recognition. Current geometric…

Large language models (LLMs) achieve state-of-the-art results across many natural language tasks, but their internal mechanisms remain difficult to interpret. In this work, we extract, process, and visualize latent state geometries in…

To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME)…

Large Language Models (LLMs) have demonstrated strong performance across a wide range of tasks, yet they still struggle with complex mathematical reasoning, a challenge fundamentally rooted in deep structural dependencies. To address this…

We introduce a graph-aware autoencoder ensemble framework, with associated formalisms and tooling, designed to facilitate deep learning for scholarship in the humanities. By composing sub-architectures to produce a model isomorphic to a…

Due to the advantages such as high security, high privacy, and liveness recognition, vein recognition has been received more and more attention in past years. Recently, deep learning models, e.g., Mamba has shown robust feature…

Programming languages possess rich semantic information - such as data flow - that is represented by graphs and not available from the surface form of source code. Recent code language models have scaled to billions of parameters, but model…

Active area of research in AI is the theory of manifold learning and finding lower-dimensional manifold representation on how we can learn geometry from data for providing better quality curated datasets. There are however various issues…

Motivation: Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse and complex molecular and biomolecular datasets due to the limited…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

Graph neural networks (GNNs) on text--attributed graphs (TAGs) typically encode node texts using pretrained language models (PLMs) and propagate these embeddings through linear neighborhood aggregation. However, the representation spaces of…

Learning disentangled representations is regarded as a fundamental task for improving the generalization, robustness, and interpretability of generative models. However, measuring disentanglement has been challenging and inconsistent, often…

Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…

Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its…

We present a general framework of semi-supervised dimensionality reduction for manifold learning which naturally generalizes existing supervised and unsupervised learning frameworks which apply the spectral decomposition. Algorithms derived…

We propose a paradigm for interpretable Manifold Learning for scientific data analysis, whereby we parametrize a manifold with $d$ smooth functions from a scientist-provided dictionary of meaningful, domain-related functions. When such a…